An acoustic positioning system is used to establish the georeferenced and instantaneous absolute position of a fixed or mobile beacon. Amongst the known global acoustic positioning systems, the systems that are known as Ultra Short Baseline—USBL and the systems known as Short Baseline—SBL usually comprise a network of N acoustic sensors or hydrophones placed in a 2D or 3D antenna structure. This antenna is used to determine the relative position of a sound source or beacon emitting a deterministic acoustic signature. The measurement of the travelling times of the sound wave from the source to the sensors (TOA—Time Of Arrival) and/or the measurement of phase (POA—Phase Of Arrival) make it possible to determine the relative position of the beacon. The use of an attitude unit (supplying the parameters: Roll (R), Yaw (L), and Pitch (T)), compensating for the effects of the movements of the antenna on the positioning, associated with an item of georeferencing information (GPS—Global Positioning System), makes it possible to determine the absolute position of the beacon. The positioning cycle, called recurrence, is reiterated periodically to provide each time a new estimate of the absolute position of the beacon. French Patent 2.851.340 proposes a global positioning system of the USBL type. The accuracy of the USBL systems (and that of the SBL systems) is partly dependent on the dimension of the antenna structure. The typical distance between the sensors of the antenna is less than or equal to 0.5 m in the context of the USBL and is greater than a meter in the context of the SBL. The accuracy of a positioning antenna of this type is defined as follows:
                              σ          θ                =                  λ                      d            ⁢                                                  ⁢            π            ⁢                                                  ⁢                          cos              ⁡                              (                θ                )                                      ⁢                                          2                ⁢                                                                  ⁢                η                                                                        1        ⁢                  -                ⁢        1            
In this formula, λ is the wavelength defined as the ratio between the velocity c in the water layer of the antenna and the carrier frequency F0. The angle of incidence of the sound wave e on the antenna, the signal-to-noise ratio η and the distance d between the sensors determine the accuracy of positioning of the USBL system. In addition to the environmental parameters (noise level, velocity, etc.) and the application parameters (signal level, carrier frequency, angle of incidence, etc.), the dimension of the antenna determines the accuracy of the positioning system.